Making a site accessible and usable for some types of disabilities is fairly straightforward. For visual impairments and motor impairments, there are a few things to think about (text equivalents, meaningful link texts, clear visual feedback for keyboard navigation, etc.). When it comes to other disabilities, like dyslexia, autism, and cognitive disabilities, things get more complicated.
For AAA compliance you need to know quite a lot about about these things, and others. You need to be able to create video clips with the important content translated into sign language. You need to have graphic representations (pictograms) of the content for those who cannot read text at all. You also need to write text that can be read by anyone, including those with severe dyslexia or cognitive disabilities. You need to understand those disabilities to create visual designs that do not hinder their understanding of a site, but help it.
For A and AA, much (but not all) of the required skills are technical. It's basically what you do in code. For AAA you need to know a lot more about different disabilities. You need to have language skills that go beyond what we learn in school. You need to understand how, e.g., people with Down's syndrome interact with a web site. And so on.
XHTML vs HTML FAQ. This issue is off-topic in this thread, anyway.